Discrete modeling of deterministic size effect of normal-strength and ultra-high performance concrete under compression

Size effect of heterogeneous granular materials under tensile loading is a well known phenomenon and the subsequent size effect laws are widely available in the scientific literature. On the contrary, size effect in compression is scarcely studied, which, especially for concrete, is more significant for its brittle failure mode in practical applications. This paper investigates the deterministic size effect in compression of concretes including a normal strength concrete (NSC) and an ultra high performance concrete (UHPC). The Lattice Discrete Particle Model (LDPM) is selected to determine the compressive strength of a broad range of sizes utilizing experimental-based calibrated data sets. The simulated tests include both cylinders and prisms with the diameter/width range from 150 mm to 600 mm for normal strength concrete and from 50 mm to 200 mm for UHPC. The investigated aspect ratio ranges from 1 to 16. It is found that the simulated strengths show no size effect under low friction loading, and the magnitude of size effect decreases with rising aspect ratio under high friction loading. The size effect laws available in the literature are not able to fit the obtained compressive strength data and a new compressive size effect law formula named ComSEL3D is proposed in terms of diameter and aspect ratio. The correlation by ComSEL3D for the simulated strengths is above 0.99, which shows its excellent ability in describing and predicting the deterministic size effect behavior in compression for both concretes in cylindrical and prism shapes. The ComSEL3D also outperforms the available formulas in the literature in matching the experimental results of various concretes under compression.